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Question

A point on the ellipse 4x2+9y2=36, where the normal is parallel to the line 4x−2y−5=0, is?

A
(85,95)
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B
(95,85)
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C
(95,85)
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D
(85,95)
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Solution

The correct option is D (95,85)
Let P(x1,y1), be the point on curve 4x2+9y2=36, where the normal is parallel to line 4x2y=5.
dydx|p(x1,y1)=(4x19y1)
Now, 9y14x1=29y1=8x1..(1)
Also, 4x21+9y21=36 (2)
On solving (1) and (2), we get
P(x1=95,y1=85) or (x1=95,y1=85).

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